"Lena Dunham has been coming up a lot lately in my therapy sessions," blogged filmmaker Desiree Akhavan in March 2013. "We're too damn similar and she beat me to the punch." Dunham either read her frustrated tirade or the pair are as cosmically intertwined as their identical career-paths suggest: it has been announced that she has signed Akhavan up for the fourth series of her HBO series, Girls.

Both Akhavan and another newcomer, Peter Mark Kendall, will play Hannah's fellow attendees at the Iowa Writers' Workshop, but it was a while before the casting announcement that Dunham and Akhavan were mentioned in the same breath. When Akhavan's comedy Appropriate Behaviour – about a bisexual young woman struggling to become the ideal Persian daughter – premiered at the most recent Sundance film festival, critics immediately spotted similarities with Dunham's debut, Tiny Furniture. Both films are set in Brooklyn and focus on their misfit protagonists' struggle with jobs and relationships (or rather, their lack of these things). And, despite Akhavan's protestations that her film is more Annie Hall than Hannah Horvath, she was dubbed "the next Lena Dunham" by interviewer after interviewer.

Both women started their careers by producing web comedy. Akhavan's The Slope, co-produced with her then-partner, Ingrid Jungermann, follows the rocky relationship of two self-professed "homophobic, shallow lesbians". Dunham's webseries, Delusional Downtown Divas, was a self-parody too – but of her set's art-world lifestyle. Dunham's The Fountain shows her bathing and brushing her teeth in Oberlin College fountain, and won her plenty of cruel YouTube comments and thousands of hits, an experience she then wrote into the script of Tiny Furniture. Akhavan is equally no stranger to using embarrassment as comedy material – when she was voted "ugliest girl in school" in the eighth grade, her first reaction was, "Oh, I'm going to use this."

Perhaps what sets Akhavan apart from even Dunham is that she is not only bisexual, but Iranian. In the words of her college professor she is "the gay, Iranian Lena Dunham". While Dunham's career has always been two steps ahead, Akhavan's work cannot be accused of being "too white and straight", a criticism she acknowledges has been levelled at Dunham.

Appropriate Behaviour, shot on a shoestring in only 18 days, charts the experiences of Shirin, who feels she cannot come out to her traditional family. The film's title references her hapless attempts to appease this family while living as a sexually liberated twentysomething. Akhavan, like Dunham, sees frank, on-screen sex as a priority. "I feel like a lot of scenes graze over sex and make it this silky smooth thing," she told Variety. Her work examines race and female LGBTQ experience, issues some argued were missing from Girls in previous seasons (though it remains to be seen whether Akhavan's character will be bisexual).

Whether Dunham felt threatened by critics' comparisons or benevolent towards her rival, she's keeping Akhavan close. On Twitter yesterday she wrote: "[Akhavan]'s the very best! Stay tuned for some true gothique joy in the form of her character". (To which Akhavan replied, "I will wear the eyeliner and hope it doesn't wear me.") And we can only assume Akhavan's perceived bitterness towards Dunham (always done with her tongue in her cheek) has now abated. Whatever the case, the homemade meme which accompanied Akhavan's 2013 blogpost, featuring her own face Photoshopped into a picture of the Girls cast, now seems spookily prescient.

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